Halacha forbids deriving personal benefit from any of the sacred articles of the Bet Ha'mikdash, and from the Bet Ha'mikdash itself, due to their unique status of sanctity. For this reason, the Rambam writes (Hilchot Me'ila 8:3) that the formal Halachic status of Kedusha (sanctity) was conferred upon the Temple only after its construction was completed. Had the materials been endowed with Halachic sanctity already from the outset, then the builders would have transgressed the prohibition of Me'ila – deriving personal benefit from sacred property – during the building process, when they would use the walls for shelter from the sun or rain.
Does this prohibition apply nowadays to the Western Wall in Jerusalem, which is part of the wall that surrounds the Temple Mount? Is it permissible for a visitor to take a pebble from one of the cracks in the Wall as a souvenir, or does this violate the prohibition of Me'ila?
Rabbi Moshe Feinstein (Russia-New York, 1895-1986) addresses this question in his Iggerot Moshe (Y.D. 4:63), and he writes unequivocally that one may not derive any personal benefit from the stones of the Western Wall, as doing so transgresses the prohibition of Me'ila. He argues that the sanctity of the Temple extends even to the wall surrounding the Temple Mount, and thus the Western Wall, like the Temple itself, is subject to the Me'ila prohibition. Even after the Temple's destruction, the Western Wall's special status of Kedusha remains, as the Rabbis comment, "The Shechina [Divine Presence] never departed from the Western Wall." Therefore, it remains subject to the law of Me'ila even in the absence of a Temple.
Rabbi Feinstein adds that one who takes a pebble from the Western Wall violates another prohibition, as well, that of "Lo Ta'asun Kein Le'Hashem Elokeichem" (Devarim 12:4), which forbids destroying sacred articles. The Rama (Rabbi Moshe Isserles, Poland, 1525-1572), in his glosses to the Shulchan Aruch (O.C. 152), applies this prohibition even to the destruction of a synagogue; he rules that it is forbidden to destroy a synagogue except for the purpose of building another one in its place. By the same token, Rabbi Feinstein writes, it would be forbidden to take even a small pebble from the Western Wall, and this amounts to "dismantling" the sacred wall surrounding the Temple Mount.
Thus, one may not take a pebble from the Western Wall, due to both the prohibition of Me'ila and the law forbidding any kind of dismantling of sacred articles.